Ukraine's new prime minister Arseniy Yatsenyuk says his country is refusing to respond with force to what he calls Russian "provocation" in Crimea.

The increasing instability in Ukraine has seen Western powers including Britain and the United States call for an urgent de-escalation of tensions.

"The inadequate presence of Russian troops on Ukrainian territory is a provocation, and Russian attempts to make Ukraine react with force have failed," Mr Yatsenyuk said at a televised cabinet meeting.

"It is unacceptable when armoured Russian military vehicles are out in the centre of Ukrainian towns.

"We do not give in to provocative actions, we do not use force and we demand that Russia stop its provocative actions and return the troops to base."

The prime minister's comments came as Russian president Vladimir Putin sought approval to move armed forces into Ukrainian territory.

Seven things to know about Crimea

The Crimean Peninsula is rich in arable land and occupies a strategically important location on the Black Sea.

Crimea has a population of 2.3 million, 58 per cent of whom speak Russian and identify themselves as ethnic Russians.

The Soviet Union transferred authority over Crimea to Ukraine in 1954.

Ukraine retained control after the collapse of the USSR in a 1994 agreement brokered by the US, UK and France.

Russia's major naval base is located in Sevastopol and is the base for their Black Sea Fleet. Russia's lease on the base expires in 2042.

The lease states that Russian personnel may not remove military equipment or vehicles outside the base without permission from Ukraine.

The region was a stronghold for ousted president Viktor Yanukovych.

Defence minister Igor Tenyukh told the cabinet meeting that Russia began sending these reinforcements on Friday "without warning or Ukraine's permission, in defiance of the principle of non-infringement of state borders."

The US ambassador to the United Nations, Samantha Power, says Ukraine's new government has to be allowed to do its work.

"The United States would condemn any move to undermine Ukraine's sovereignty or territorial integrity which we expect all states to respect," she said.

"The best way for the people of Crimea to achieve their goals is to work peacefully within the established political system.

"To this end the United States calls for an urgent international mediation mission to the Crimea to begin to de-escalate the situation."

British foreign secretary William Hague will visit Kiev on Sunday for talks with the interim Ukrainian government, a British foreign office spokesman said.

The spokesman had no further details about the trip, but Mr Hague tweeted: "Have just spoken to Acting President [Oleksandr] Turchynov. I will travel to Kiev on Sunday for talks with the new government."

Mr Hague also spoke to his Russian counterpart Sergei Lavrov and called for a "de-escalation" of tensions.

Putin requests use of armed forces amid pro-Russian rallies

Mr Putin on Saturday submitted a request to the upper house of parliament asking for approval for the use of Russian troops in Ukraine, the Kremlin said.

"In connection with the extraordinary situation in Ukraine and the threat to the lives of Russian citizens... I submit to the Federation Council a request to use the armed forces of the Russian Federation on Ukrainian territory until the normalisation of the political situation in that country," the Kremlin quoted Mr Putin as saying in the document.

Russia's parliament, flying in the face of US president Barack Obama's warning against any Russian intervention, had earlier urged Mr Putin to "to take measures to stabilise the situation in Crimea and use all available means to protect the people of Crimea from tyranny and violence".

More than 10,000 people carrying Russian flags were protesting on Saturday in the eastern Ukrainian city of Donetsk, the stronghold of ousted president Viktor Yanukovych, an AFP journalist said.

Protesters declared they supported "the aspirations of Crimea to rejoin Russia".

"Russia! Russia!", they shouted, as demonstrators on the sidelines of the rally distributed leaflets calling on people "not to obey authorities in Kiev".

"We're aghast by what is happening in Kiev," Oleksandr, a 40-year-old protester, said.

"We will not let nationalists enter our city."

Any Russian intervention will be costly: Obama

On Friday, Mr Obama issued a warning to Russia that "there will be costs" for any military intervention in neighbouring Ukraine.

"We are now deeply concerned by reports of military movements taken by the Russian Federation inside of Ukraine," he said.

"Any violation of Ukraine's sovereignty and territorial integrity would be deeply destabilising, which is not in the interest of Ukraine, Russia or Europe.

"It would represent a profound interference in matters which must be determined by the Ukrainian people. It would be a clear violation of Russia's commitment to respect the independence and sovereignty and borders of Ukraine, and of international laws.

"The United States will stand with the international community in affirming that there will be costs for any military intervention in Ukraine."

He provoked protests in Ukraine in November by backing out of plans to sign landmark deals with the European Union and instead saying Kiev would seek closer economic and trade ties with its former Soviet master Russia.